Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model

Abstract

In portfolio optimization problems, the minimum expected investment risk is not always smaller than the expected minimal investment risk. That is, using a well-known approach from operations research, it is possible to derive a strategy that minimizes the expected investment risk, but this strategy does not always result in the best rate of return on assets. Prior to making investment decisions, it is important to an investor to know the potential minimal investment risk (or the expected minimal investment risk) and to determine the strategy that will maximize the return on assets. We use the self-averaging property to analyze the potential minimal investment risk and the concentrated investment level for the strategy that gives the best rate of return. We compare the results from our method with the results obtained by the operations research approach and with those obtained by a numerical simulation using the optimal portfolio. The results of our method and the numerical simulation are in agreement, but they differ from that of the operations research approach.

37 pages, 1 figure

References in corpus (3)

• The large deviation approach to statistical mechanics
• Risk Minimization through Portfolio Replication
• On analyticity with respect to the replica number in random energy models I: an exact expression of the moment of the partition function

Cited by in corpus (9)

• Minimal Investment Risk of Portfolio Optimization Problem with Budget and Investment Concentration Constraints
• Replica Analysis for the Duality of the Portfolio Optimization Problem
• Portfolio Optimization Problem with Non-identical Variances of Asset Returns using Statistical Mechanical Informatics
• Random matrix approach for primal-dual portfolio optimization problems
• Replica Analysis for Portfolio Optimization with Single-Factor Model
• Replica Approach for Minimal Investment Risk with Cost
• Minimal Investment Risk with Cost and Return Constraints: A Replica Analysis
• Property Safety Stock Policy for Correlated Commodities Based on Probability Inequality
• Pythagorean theorem of Sharpe ratio